Recent content by daswerth

It just occurred to me that this may be simpler than I thought. The obvious mapping would be simply to send the homomorphism to the n-tuple that it assigns its unit vectors to. I had assumed the map would be more complicated/interesting. I'm going to investigate whether this map is bijective.

Homework Statement Consider the set Hom of homomorphisms from \mathbb{Z}^n (the n-dimensional integer lattice) to a group G . Also let S = \left\{ \, ( g_1, g_2, \dots, g_n ) \, | \, g_i g_k = g_k g_i, \text{where} \, 0 < i,k \leq n, g_i \in G \right\}, the set of n-tuples from G...